Cooperativity of the phase transition in single- and multibilayer lipid vesicles.

The effect of membrane morphology on the cooperativity of the ordered-fluid, lipid phase transition has been investigated by comparing the transition widths in extended, multibilayer dispersons of dimyristoyl phosphatidyl-choline, and also of dipalmitoyl phosphatidylcholine, with those in the small, single-bilayer vesicles obtained by sonication. The electron spin resonance spectra of three different spin-labelled probes, 2,2,6,6-tetramethylpiperdine-N-oxyl, phosphatidylcholine and stearic acid, and also 90 degrees light scattering and optical turbidity measurements were used as indicators of the phase transition. In all cases the transition was broader in the single-bilayer vesicles than in the multibilayer dispersions, corresponding to a decreased cooperativity on going to the small vesicles. Comparison of the light scattering properties of centrifuged and uncentrifuged, sonicated vesicles suggests that these are particularly sensitive to the presence of intermediate-size particles, and thus the spin label measurements are likely to give a more reliable measure of the degree of cooperativity of the small, single-bilayer vesicles. Application of the Zimm and Bragg theory ((1959) J. Chem. Phys. 31, 526-535) of cooperative transitions to the two-dimensional bilayer system shows that the size of the cooperative unit, 1/square root sigma, is a measure of the mean number of molecules per perimeter molecule, in a given region of ordered or fluid lipid at the centre of the transition. From this result it is found that it is the vesicle size which limits the cooperativity of the transition in the small, single-bilayer vesicles. The implications for the effect of membrane structure and morphology on the cooperativity of phase transitions in biological membranes, and for the possibility of achieving lateral communication in the plane of the membrane, are discussed.     

Cooperativity of the phase transition in single- and multibilayer lipid vesicles

The effect of membrane morphology on the cooperativity of the ordered-fluid, lipid phase transition has been investigated by comparing the transition widths in extended, multibilayer dispersions of dimyristoyl phosphatidylcholine, and also of dipalmitoyl phosphatidylcholine, with those in the small, single-bilayer vesicles obtained by sonication. The electron spin resonance spectra of three different spin-labelled probes, $\text{2,2,6,6-}\text{tetramethylpiperdine}\text{-N-}\text{oxyl}$, phosphatidylcholine and stearic acid, and also 90° light scattering and optical turbidity measurements were used as indicators of the phase transition. In all cases the transition was broader in the single-bilayer vesicles than in the multibilayer dispersions, corresponding to a decreased cooperativity on going to the small vesicles. Comparison of the light scattering properties of centrifuged and uncentrifuged, sonicated vesicles suggests that these are particularly sensitive to the presence of intermediate-size particles, and thus the spin label measurements are likely to give a more reliable measure of the degree of cooperativity of the small, single-bilayer vesicles. Application of the Zimm and Bragg theory ((1959) J. Chem. Phys. 31, 526–535) of cooperative transitions to the two-dimensional bilayer system shows that the size of the cooperative unit, 1/?σ, is a measure of the mean number of molecules, per perimeter molecule, in a given region of ordered or fluid lipid at the centre of the transition. From this result it is found that it is the vesicle size which limits the cooperativity of the transition in the small, single-bilayer vesicles. The implications for the effect of membrane structure and morphology on the cooperativity of phase transitions in biological membranes, and for the possibility of achieving lateral communication in the plane of the membrane, are discussed.     

How noise and coupling influence leading indicators of population extinction in a spatially extended ecological system

Anticipating critical transitions in spatially extended systems is a key topic of interest to ecologists. Gradually declining metapopulations are an important example of a spatially extended biological system that may exhibit a critical transition. Theory for spatially extended systems approaching extinction that accounts for environmental stochasticity and coupling is currently lacking. Here, we develop spatially implicit two-patch models with additive and multiplicative forms of environmental stochasticity that are slowly forced through population collapse, through changing environmental conditions. We derive patch-specific expressions for candidate indicators of extinction and test their performance via a simulation study. Coupling and spatial heterogeneities decrease the magnitude of the proposed indicators in coupled populations relative to isolated populations, and the noise regime and the degree of coupling together determine trends in summary statistics. This theory may be readily applied to other spatially extended ecological systems, such as coupled infectious disease systems on the verge of elimination.     

GUVs Melt Like LUVs: The Large Heat Capacity of MLVs Is Not Due to Large Size or Small Curvature

The excess heat capacity functions (ΔC_p) associated with the main phase transition of large unilamellar vesicles (LUVs) and multilamellar vesicles (MLVs) are very different. Two explanations are possible. First, the difference in vesicle size (curvature) results in different gel-fluid interactions in the membrane; those interactions have a large effect on the cooperativity of the phase transition. Second, there is communication between the bilayers in an MLV when they undergo the gel-fluid transition; this communication results in thermodynamic coupling of the phase transitions of the bilayers in the MLV and, consequently, in an apparent increase in the cooperativity of the transition. To test these hypotheses, differential scanning calorimetry was performed on giant unilamellar vesicles (GUVs) of pure dipalmitoylphosphatidylcholine. The ΔC_p curve of GUVs was found to resemble that of the much smaller LUVs. The transition in GUVs and LUVs is much broader (half-width ∼1.5°C) than in MLVs (∼0.1°C). This similarity in GUVs and LUVs indicates that their size has little effect on gel-fluid interactions in the phase transition. The result suggests that coupling between the transitions in the bilayers of an MLV is responsible for their apparent higher cooperativity in melting.     

The Dipole Model and Phase Transitions in Biological Membranes

Assuming the dipole model for a membrane, approximate calculations are made which employ a dipole-dipole interaction energy. The calculations are based upon the assumption of cooperative coupling of membrane polar molecules and make use of the Bragg-Williams approximation. A theoretical estimate is made of the critical temperature at which phase changes might occur in certain biological membranes. Proposals are presented which explain how the dipole transition might relate to the sometimes observed thermal phase transitions in biological membranes.     

构象电子系统的集体激发,跃迁过程和合作现象

本文给出了一套对分子生物学问题进行理论分析的方法并列举简单应用的实例.以分子构象和前沿电子为变数,引入了构家电子场,给出了研究其集体激发的Green函数途径,指出生物凝聚态中存在新型局域激发.导出了构象电子跃迁哈密顿量,特别研究了光致构家电子跃迁,指出低阶跃迁为非Franck—Condon型的.研究了链式分子的合作现象,阐明了振动激发对于实现合作转变的重要性及转变中可能存在反常温度依赖.     

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two‐state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non‐cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier‐less “downhill” folding, as well as for continuous “uphill” unfolding transitions, indicate that gradual non‐cooperative processes may be ubiquitous features on the free energy landscape of protein folding.     

The ‘n’ effect in molecular recognition

The cooperativity which exists in crystal melting and many biological molecular recognition phenomena arises from extended arrays of weak interactions. We present a correlation between the melting temperature of a crystal and the intermolecular energy (which is evident only when compounds possessing several or many internal rotors are excluded). The correlation is used as the basis for a model of crystal melting which is capable of estimating the melting temperature of crystals. This model provides the basis for an understanding of the sharpness of the crystal melting transition for organic and inorganic substances. The cooperativity illustrated by the extended arrays of weak interactions, or the ‘n’ effect, is extended to analogous order/disorder transitions in biological systems, such as the ‘melting’ of DNA and RNA duplexes, providing insights into the physical properties of these structures.     

Variability of bursting patterns in a neuron model in the presence of noise

Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of interspikes for most parameter values. As the parameter of activation kinetics of a slow potassium current is shifted to more hyperpolarized values of the membrane potential, the model undergoes a sequence of incremental spike adding transitions accumulating towards a periodic tonic spiking activity. Within a narrow parameter window around every spike adding transition, spike alteration of bursting is deterministically chaotic due to homoclinic bifurcations of a saddle periodic orbit. We have found that near these transitions the interneuron model becomes extremely sensitive to small random perturbations that cause a wide expansion and overlapping of the chaotic windows. The chaotic behavior is characterized by positive values of the largest Lyapunov exponent, and of the Shannon entropy of probability distribution of spike numbers per burst. The windows of chaotic dynamics resemble the Arnold tongues being plotted in the parameter plane, where the noise intensity serves as a second control parameter. We determine the critical noise intensities above which the interneuron model generates only irregular bursting within the overlapped windows.     

Design Principles of a Genetic Alarm Clock

Turning genes on and off is a mechanism by which cells and tissues make phenotypic decisions. Gene network motifs capable of supporting two or more steady states and thereby providing cells with a plurality of possible phenotypes are referred to as genetic switches. Modeled on the bases of naturally occurring genetic networks, synthetic biologists have successfully constructed artificial switches, thus opening a door to new possibilities for improvement of the known, but also the design of new synthetic genetic circuits. One of many obstacles to overcome in such efforts is to understand and hence control intrinsic noise which is inherent in all biological systems. For some motifs the noise is negligible; for others, fluctuations in the particle number can be comparable to its average. Due to their slowed dynamics, motifs with positive autoregulation tend to be highly sensitive to fluctuations of their chemical environment and are in general very noisy, especially during transition (switching). In this article we use stochastic simulations (Gillespie algorithm) to model such a system, in particular a simple bistable motif consisting of a single gene with positive autoregulation. Due to cooperativety, the dynamical behavior of this kind of motif is reminiscent of an alarm clock – the gene is (nearly) silent for some time after it is turned on and becomes active very suddenly. We investigate how these sudden transitions are affected by noise and show that under certain conditions accurate timing can be achieved. We also examine how promoter complexity influences the accuracy of this timing mechanism.     

T helper cell polarization and the generation of varied antigen-dependent immune responses: a Markov chain model.

BACKGROUND: Adaptive immune responses are deterministically classified into humoral or cell-mediated depending on the pattern of Th cell polarization into Th1 or Th2. Evidence suggests that the process of Th polarization is stochastic, however, the presence of some deterministic components has not been ruled out. Here, a Markov chain model that accounts for Th-mediated immune responses was developed based on the assumption that Th polarization and consequent transition events are stochastic. RESULTS: Using assumed probability values, model analysis suggests that there is a rapid convergence to produce an immune response once the Th cell is stimulated by an antigen which is amplified as the number of transitions increases. The expected number of visits between Th and itself, B and itself and Tc and itself is about one whereas it is zero, less than one or degrees in the rest of the transition events depending on the interacting states. CONCLUSIONS: Based on model analysis and validation, modeling Th-mediated immune responses as a Markov chain process seems to be plausible. The large degree of flexibility inherent in such a view of adaptive immunity can be helpful in addressing questions pertinent to Th function and behavior.     

The effect of photoreceptor coupling and synapse nonlinearity on signal:noise ratio in early visual processing

Electrical coupling of vertebrate photoreceptors is well known to improve the signal: noise ratio in the photoreceptor layer for large-area stimuli. For example, if N photoreceptors are perfectly coupled to each other, the signal: noise ratio is improved for stimuli illuminating more than a number M = square root of N of the receptors but is made worse for small-area stimuli illuminating less than M of the N receptors. Using the model of Lamb & Simon (J. Physiol., Lond. 263, 257 (1976], which treats the photoreceptor layer as a square array of cells, each coupled through a resistive gap junction to the four cells around it, we show that the signal:noise ratio for small-area stimuli is much greater than would be expected from a model in which receptors are assumed to be perfectly coupled. Contrary to predictions made assuming perfect coupling, receptor coupling should not prevent rods from detecting single photons, but whether the single photon signal can be detected at the bipolar cell level depends on how signals are read out of the receptor layer. The signal:noise ratio in bipolar cells postsynaptic to the photo-receptor layer is determined partly by synaptic convergence and nonlinearity in synaptic transmission from receptors. If the synaptic gain decreases with light-induced receptor hyperpolarization, as is found experimentally, then receptor coupling can improve the postsynaptic signal:noise ratio for stimuli illuminating only one receptor, even though coupling decreases the presynaptic signal:noise ratio for such stimuli. Moreover, increasing the number of coupled receptors projecting to a bipolar cell can improve the signal:noise ratio for localized stimuli if the synapse is sufficiently nonlinear (although, for the degree of nonlinearity seen in lower vertebrates, synaptic convergence makes the ratio worse for the single photon event). The fact that receptor coupling and synaptic convergence can, under some circumstances, improve the signal:noise ratio in bipolar cells suggests a principle of retinal design that may compete with the requirements of high spatial resolution.     

Model for cooperativity of biological membranes

We present a mathematical model for the complex cooperativity observed in biological membranes. In our model, it is assumed that the proteins bound on the membrane are noncooperative and possess a Bohr proton. It is further assumed that the net charge of the unliganded state of the protein is different from that of the liganded state owing to the structural change upon binding the ligand. With this model, we show how an all-or-none response, a graded response, and a noncooperative response arise in the binding curve of such biological membranes. In addition, we show how an effector, which can alter the pK_a involved in the binding site, induces a complex cooperativity.     

Noise and Information Transmission in Promoters with Multiple Internal States

Based on the measurements of noise in gene expression performed during the past decade, it has become customary to think of gene regulation in terms of a two-state model, where the promoter of a gene can stochastically switch between an ON and an OFF state. As experiments are becoming increasingly precise and the deviations from the two-state model start to be observable, we ask about the experimental signatures of complex multistate promoters, as well as the functional consequences of this additional complexity. In detail, we i), extend the calculations for noise in gene expression to promoters described by state transition diagrams with multiple states, ii), systematically compute the experimentally accessible noise characteristics for these complex promoters, and iii), use information theory to evaluate the channel capacities of complex promoter architectures and compare them with the baseline provided by the two-state model. We find that adding internal states to the promoter generically decreases channel capacity, except in certain cases, three of which (cooperativity, dual-role regulation, promoter cycling) we analyze in detail.     

On the displacement of cooperative transitions of linear biopolymers by an electric field

A basic theory for equilibrium properties of cooperative transitions (particularly helix–coil transformations) of sufficiently long linear biopolymers under the influence of an electric field is developed. General relations for the calculation of the distribution of uninterrupted sequences of elementary subunit states (e.g., helical fragments) as well as the overall degree of transition θ are given. Strong cooperativity is found to permit simplifications. It is shown that only in this case can a practically significant field effect be expected. Numerical results are presented for a special example of experimental interest.     

Evaluation of cooperativity for phase transitions in two- and three-dimensional systems

Use of the so-called "cooperative unit" (readily obtainable from the midpoint slope of phase transition curves) is discussed for the determination of cluster sizes and cooperative interaction energies. This quantity has been commonly employed in a rather empirical way since its correct interpretation is known only for some special cases (linear systems, all-or-none transitions). It is shown in the framework of a lattice model (Ising model) that the cooperative unit may be interpreted in terms of correlation functions and that it defines an average cluster corresponding to the patch size as obtained from scattering experiments. Relations between the cooperative unit and a cooperativity parameter are given for various lattices. Different types of transition curves are discussed using a simple analytical formalism, the quasichemical approximation. Some important nonideality effects are investigated which may lead to a "smearing-out" of first-order transitions.